Yes, St. Augustine speaks a great deal about final perseverance, and St. Benedict's Centre says they believe as he did: "Saint Augustine taught, as is clear from this article’s epigram, that the providence of God would see to it that a justified catechumen would be baptized before death. God alone, in any event, knows which of those, with a votum for baptism and perfect contrition, He has justified. The Church can only assume, as the arm of Christ, the Principal Agent in baptism, that all are in need of receiving the sacramentin order to not only have all sin forgiven and abolished, but to be a member of the Church, the Body of Christ. Anticipating the rejoinder that no one is lost who dies in the state of grace, let me just affirm that I agree. Not only that I agree, but that I submit to this truth as I would a dogma of Faith. The Church, however, allows the faithful the freedom to believe that the providence of God will see to it that every person dying in the state of grace will also be baptized. This preserves the literal sense of Christ’s teaching in John 3:5: “Amen, amen I say to thee, unless a man be born again of water and the Holy Ghost, he cannot enter into the kingdom of God” and His apostolic mandate to preach and baptize all nations in Mark 16: 15-16." A way to formulate this would be, someone who believes in Christ and makes an act of love of God, united with the desire of the Sacraments, can obtain or return to justification and the state of sanctifying grace; and if he perseveres in striving to love God and keep His commandments, above all in prayer, he will be given final perseverance by God after he has become Catholic.
And for those who opposed what I said earlier that the Eucharist is the great pledge of obtaining final perseverance, listen to St. Augustine's exegesis of the Lord's prayer, "The fourth petition is, Give us this day our daily bread, Matthew 6:11 where the blessed Cyprian shows how here also perseverance is understood to be asked for. Because he says, among other things, And we ask that this bread should be given to us daily, that we who are in Christ, and daily receive the Eucharist for the food of salvation, may not by the interposition of some heinous sin be separated from Christ's body by being withheld from communicating and prevented from partaking of the heavenly bread. These words of the holy man of God indicate that the saints ask for perseverance directly from God, when with this intention they say, Give us this day our daily bread, that they may not be separated from Christ's body, but may continue in that holiness in which they allow no crime by which they may deserve to be separated from it ...If, therefore, it be granted to him according to his prayer that he may not be led, certainly by the gift of God he persists in that sanctification which by the gift of God he has received."
http://www.newadvent.org/fathers/15122.htmSince final perseverance is a separate grace, to be obtained above all by the Sacraments and by prayer, receiving justification is not a guarantee that anyone will persevere. It is the gift of grace to anyone that he or she does persevere in faith and love until the end.
Ladislaus, I think SBC doesn't worry very much about whether or not a Protestant is in material heresy, and admits he may be one for a while. I read their website a while ago, that's if I remember correctly. I have no issue with that. But I think Cardinal Billot is right here (and also to clear up a possible misunderstanding - Cardinal Billot is talking about Catholics in the section you quoted, he is saying Catholics mistaken about a matter of fact are not material heretics; the term material heretics, according to +Billot, is reserved for Protestants in material heresy; Canon Law also speaks of "heretics who err in good faith" who are to be denied the Sacraments) and you will find similar sentiments in Cardinal Franzelin, Cardinal Lugo etc. This is Cardinal Lugo in De Virtute Fidei divinae, "Others acknowledge the Triune God and Christ, as most heretics do… Now if these people are excused from the sin of infidelity by reason of invincible ignorance, they can be saved. For those who are in invincible ignorance about some articles of faith but believe others, are not formally heretics, but they have supernatural faith, by which they believe true articles, and on this basis there can follow acts of perfect contrition, by which they can be justified and saved ... One who is baptized as an infant by heretics, and is brought up by them in false doctrine, when he reaches adulthood, could for some time not be guilty of sin against the Catholic faith, as long as this had not been proposed to him in a way sufficient to oblige him to embrace it. However, if the Catholic faith were subsequently proposed to him in a way sufficient to oblige him to embrace it and to abandon errors contrary to it, and he still persisted in his errors, then he would be a heretic.” When Cardinal Billot says "there is no scope for heresy, even materially", he's saying erring Catholics are not material heretics.
Anyway, I'm not much interested in getting into a debate on that. What is necessary imho is (1) to believe Protestants, and others, should become Catholic to be saved and (2) to pray, work and sacrifice for their conversion and salvation. Some do not believe 1 very strongly, but still do 2. Some believe 1, but neglect 2. Let us do both, omitting nothing, and then we will be perfect disciples of Christ.